The effect of finite temperature T and finite strain rateγ on the statistical physics of plastic deformations in amorphous solids made of N particles is investigated. We recognize three regimes of temperature where the statistics are qualitatively different. In the first regime the temperature is very low, T < Tcross(N ), and the strain is quasi-static. In this regime the elasto-plastic steady state exhibits highly correlated plastic events whose statistics are characterized by anomalous exponents. In the second regime Tcross(N ) < T < Tmax(γ) the system-size dependence of the stress fluctuations becomes normal, but the variance depends on the strain rate. The physical mechanism of the crossover is different for increasing temperature and increasing strain rate, since the plastic events are still dominated by the mechanical instabilities (seen as an eigenvalue of the Hessian matrix going to zero), and the effect of temperature is only to facilitate the transition. A third regime occurs above the second cross-over temperature Tmax(γ) where stress fluctuations become dominated by thermal noise. Throughout the paper we demonstrate that scaling concepts are highly relevant for the problem at hand, and finally we present a scaling theory that is able to collapse the data for all the values of temperatures and strain rates, providing us with a high degree of predictability.
The attenuation of long-wavelength phonons (waves) by glassy disorder plays a central role in various glass anomalies, yet it is neither fully characterized, nor fully understood. Of particular importance is the scaling of the attenuation rate Γ(k) with small wavenumbers k → 0 in the thermodynamic limit of macroscopic glasses. Here we use a combination of theory and extensive computer simulations to show that the macroscopic low-frequency behavior emerges at intermediate frequencies in finite-size glasses, above a recently identified crossover wavenumber k † , where phonons are no longer quantized into bands. For k < k † , finite-size effects dominate Γ(k), which is quantitatively described by a theory of disordered phonon bands. For k > k † , we find that Γ(k) is affected by the number of quasilocalized nonphononic excitations, a generic signature of glasses that feature a universal density of states. In particular, we show that in a frequency range in which this number is small, Γ(k) follows a Rayleigh scattering scaling ∼ kd +1 (d is the spatial dimension), and that in a frequency range in which this number is sufficiently large, the recently observed generalized-Rayleigh scaling of the form ∼ kd +1 log(k0/k) emerges (k0 > k † is a characteristic wavenumber). Our results suggest that macroscopic glasses -and, in particular, glasses generated by conventional laboratory quenches that are known to strongly suppress quasilocalized nonphononic excitations -exhibit Rayleigh scaling at the lowest wavenumbers k and a crossover to generalized-Rayleigh scaling at higher k. Some supporting experimental evidence from recent literature is presented.
Identifying heterogeneous structures in glasses-such as localized soft spots-and understanding structure-dynamics relations in these systems remain major scientific challenges. Here, we derive an exact expression for the local thermal energy of interacting particles (the mean local potential energy change caused by thermal fluctuations) in glassy systems by a systematic low-temperature expansion. We show that the local thermal energy can attain anomalously large values, inversely related to the degree of softness of localized structures in a glass, determined by a coupling between internal stresses-an intrinsic signature of glassy frustration-anharmonicity and low-frequency vibrational modes. These anomalously large values follow a fat-tailed distribution, with a universal exponent related to the recently observed universal [Formula: see text] density of states of quasilocalized low-frequency vibrational modes. When the spatial thermal energy field-a "softness field"-is considered, this power law tail manifests itself by highly localized spots, which are significantly softer than their surroundings. These soft spots are shown to be susceptible to plastic rearrangements under external driving forces, having predictive powers that surpass those of the normal modes-based approach. These results offer a general, system/model-independent, physical/observable-based approach to identify structural properties of quiescent glasses and relate them to glassy dynamics.
The P2Y11-R (P2Y11 receptor) is a less explored drug target. We computed an hP2Y11-R (human P2Y11) homology model with two templates, bovine-rhodopsin (2.6 A resolution; 1 A=0.1 nm) and a hP2Y1-ATP complex model. The hP2Y11-R model was refined using molecular dynamics calculations and validated by virtual screening methods, with an enrichment factor of 5. Furthermore, mutational analyses of Arg106, Glu186, Arg268, Arg307 and Ala313 confirmed the adequacy of our hP2Y11-R model and the computed ligand recognition mode. The E186A and R268A mutants reduced the potency of ATP by one and three orders of magnitude respectively. The R106A and R307A mutants were functionally inactive. We propose that residues Arg106, Arg268, Arg307 and Glu186 are involved in ionic interactions with the phosphate moiety of ATP. Arg307 is possibly also H-bonded to N6 of ATP via the backbone carbonyl. Activity of ATP at the F109I mutant revealed that the proposed p-stacking of Phe109 with the adenine ring is a minor interaction. The mutation A313N, which is part of a hydrophobic pocket in the vicinity of the ATP C-2 position, partially explains the high activity of 2-MeS-ATP at P2Y1-R as compared with the negligible activity at the P2Y11-R. Inactivity of ATP at the Y261A mutant implies that Tyr261 acts as a molecular switch, as in other G-protein-coupled receptors. Moreover, analysis of cAMP responses seen with the mutants showed that the efficacy of coupling of the P2Y11-R with Gs is more variable than coupling with Gq. Our model also indicates that Ser206 forms an H-bond with Pgamma (the gamma-phosphate of the triphosphate chain of ATP) and Met310 interacts with the adenine moiety.
In the context of a classical example of glass-formation in 3-dimensions we exemplify how to construct a statistical mechanical theory of the glass transition. At the heart of the approach is a simple criterion for verifying a proper choice of up-scaled quasi-species that allow the construction of a theory with a finite number of 'states'. Once constructed, the theory identifies a typical scale ξ that increases rapidly with lowering the temperature and which determines the α-relaxation time τα as τα ∼ exp(µξ/T ) with µ a typical chemical potential. The theory can predict relaxation times at temperatures that are inaccessible to numerical simulations.Introduction: Among the best studied models of the glass transitions are those employing point-particles with a soft binary potential. Some repeatedly studied examples are the Kobb-Andersen model [1], the ShintaniTanaka model [2], the Dzugutov model [3] and various versions of binary mixtures with purely repulsive potentials, see for example [4,5,6]. While easy to simulate on the computer, these models are challenging for theorists due to the fact that it is extremely hard to evaluate statistical-mechanical partition-function integrals in continuous coordinates. It is therefore very tempting to find a reasonable up-scaling (coarse-graining) method that would define a discrete statistical-mechanics with partition sums rather than integrals, with the sum running on a finite number of quasi-species which have well characterized degeneracies and enthalpies. Indeed, in a number of examples in 2-dimensions it was shown that such a discrete statistical-mechanics is possible [7,8,9,10,11] and quite advantageous [12,13] in providing a successful description of the statistics and the dynamics of systems undergoing the glass transition. In this Letter we offer a general criterion for the selection of up-scaled quasispecies and demonstrate it, for the first time, in the context of a 3-dimensional model system undergoing a glass transition.
Brittle materials exhibit sharp dynamical fractures when meeting Griffith's criterion, whereas ductile materials blunt a sharp crack by plastic responses. Upon continuous pulling, ductile materials exhibit a necking instability that is dominated by a plastic flow. Usually one discusses the brittle to ductile transition as a function of increasing temperature. We introduce an athermal brittle to ductile transition as a function of the cutoff length of the interparticle potential. On the basis of extensive numerical simulations of the response to pulling the material boundaries at a constant speed we offer an explanation of the onset of ductility via the increase in the density of plastic modes as a function of the potential cutoff length. Finally we can resolve an old riddle: In experiments brittle materials can be strained under grip boundary conditions and exhibit a dynamic crack when cut with a sufficiently long initial slot. Mysteriously, in molecular dynamics simulations it appeared that cracks refused to propagate dynamically under grip boundary conditions, and continuous pulling was necessary to achieve fracture. We argue that this mystery is removed when one understands the distinction between brittle and ductile athermal amorphous materials.
Dissemination of primary tumor cells depends on migratory and invasive attributes. Here, we identify Navigator-3 (NAV3), a gene frequently mutated or deleted in human tumors, as a regulator of epithelial migration and invasion. Following induction by growth factors, NAV3 localizes to the plus ends of microtubules and enhances their polarized growth. Accordingly, NAV3 depletion trimmed microtubule growth, prolonged growth factor signaling, prevented apoptosis and enhanced random cell migration. Mathematical modeling suggested that NAV3-depleted cells acquire an advantage in terms of the way they explore their environment. In animal models, silencing NAV3 increased metastasis, whereas ectopic expression of the wild-type form, unlike expression of two, relatively unstable oncogenic mutants from human tumors, inhibited metastasis. Congruently, analyses of > 2,500 breast and lung cancer patients associated low NAV3 with shorter survival. We propose that NAV3 inhibits breast cancer progression by regulating microtubule dynamics, biasing directionally persistent rather than random migration, and inhibiting locomotion of initiated cells.
A crucially important material parameter for all amorphous solids is the yield stress, which is the value of the stress for which the material yields to plastic flow when it is strained quasistatically at zero temperature. It is difficult in laboratory experiments to determine what parameters of the interparticle potential affect the value of the yield stress. Here we use the versatility of numerical simulations to study the dependence of the yield stress on the parameters of the interparticle potential. We find a very simple dependence on the fundamental scales that characterize the repulsive and attractive parts of the potential, respectively, and offer a scaling theory that collapses the data for widely different potentials and in different space dimensions.
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